Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg


Oberseminar Differentialgeometrie


Dr. Nathan Perlmutter
Stanford University

spricht am
Montag, 24. Juli 2017
16:00 Uhr
Raum 2004 (L1)
über das Thema:

»Parametrized Morse Theory, Cobordism Categories, and Positive Scalar Curvature«

In this talk I will construct a cobordism category consisting of manifolds equipped with a choice of Morse function, whose critical points occupy a prescribed range of degrees. My main result identifies the homotopy type of the classifying space of this cobordism category with that of the infinite loopspace of a certain Thom spectrum. This result can be viewed as an analogue of the celebrated theorem of Galatius, Madsen, Tillmann and Weiss. In the second part of the talk I will show how to use the cobordism category to probe the homotopy type of the space of positive scalar curvature metrics on a closed, spin manifold of dimension ≥ 5. This construction uses a parametrized version of the Gromov-Lawson construction developed by Walsh and Chernysh. Our main result detects many non-trivial homotopy groups in the space of positive scalar curvature metrics and gives an alternative proof and slight extension of a recent breakthrough theorem of Botvinnik, Ebert, and Randal- Williams.


Hierzu ergeht herzliche Einladung.
Prof. Dr. Bernhard Hanke

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).

wwwadm@Math.Uni-Augsburg.DE,    Do 6-Jul-2017 10:39:38 MESZ